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Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann mapPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2018 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 330, p. 177-192Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Amsterdam: Elsevier, 2018. Vol. 330, p. 177-192
##### Keywords [en]

Nonlinear eigenvalue problems, Helmholtz problem, Scattering resonances, Dirichlet-to-Neumann map, Arnoldi's method, Matrix functions
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-138325DOI: 10.1016/j.cam.2017.08.012ISI: 000415783000014OAI: oai:DiVA.org:umu-138325DiVA, id: diva2:1134522
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt472",{id:"formSmash:j_idt472",widgetVar:"widget_formSmash_j_idt472",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt478",{id:"formSmash:j_idt478",widgetVar:"widget_formSmash_j_idt478",multiple:true}); Available from: 2017-08-21 Created: 2017-08-21 Last updated: 2019-05-20Bibliographically approved
##### In thesis

We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method (TIAR). Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances.

1. Reliable hp finite element computations of scattering resonances in nano optics$(function(){PrimeFaces.cw("OverlayPanel","overlay1316711",{id:"formSmash:j_idt757:0:j_idt761",widgetVar:"overlay1316711",target:"formSmash:j_idt757:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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